Multiparametric and coloured extensions of the quantum group GLq(N)GL_q(N) and the Yangian algebra Y(glN)Y(gl_N) through a symmetry transformation of the Yang-Baxter equation

Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general `symmetry transformation' of the `particle conserving' $R$-matrix is found such that the resulting multiparametric $R$-matrix, with a spectral parameter as well as a colour parameter, is also a solution of the Yang-Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and coloured extensions of the quantum group $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated.Comment: 21 pages, LaTeX (twice). Interesting physical applications of the work are indicated. To appear in Int. J. Mod. Phys.

Polynomial deformations of osp(1/2)osp(1/2) and generalized parabosons

We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of polynomial deformations of $osp(1/2)$. Irreducible representations of $R$ are described, and in the case $\deg(f)\leq 2$ we obtain a complete classification, showing some similarities but also some interesting differences with the usual $osp(1/2)$ representations. The relation with deformed oscillator algebras is discussed, leading to the interpretation of $R$ as a generalized paraboson algebra.Comment: 18 pages, LaTeX, TWI-94-X

Changes in the pattern of distribution of southwest monsoon rainfall over India associated with sunspots

Despite the systematic nature of the monsoon rains over India, large year-to-year variations in the pattern of distribution of rainfall during the season occur. The yearly pattern of rainfall distribution during the monsoon season (May 31–October 2) for each of the years 1901–51 for a network of 105 stations over India is characterized by a set of six distribution parameters. A brief description of the spatial distribution of the different patterns is given to indicate the nature of the component patterns. Polynomial trend analyses of the time series of the distribution parameters indicate oscillatory features. Power spectrum analyses reveal certain significant periods corresponding to the sunspot cycle or some higher harmonics with regional preferences. The variation of distribution parameters in the different parts of the country with the different sunspot epochs is demonstrated. Studies of the distribution of surface pressure anomalies, frequency of storms and depressions, and the frequency of “breaks in monsoon” associated with the contrasting sunspot epochs suggest that the monsoon circulation features as well as the characteristics of the rainfall distribution have a periodicity nearing the sunspot cycle

Electrochemical preparation of erythrosin and eosin

The paper highlights the preparation of erythrosin (tetra iodofluorescein) and eosin (tetra bromofluorescein) by electrolytic method at a graphite anode using a solution of sodium carbonate containing iodine and fluorescein for erythrosin and sodium bromide and fluorescein for eosin at a divided cell. The yield is compared with that of chemical method

A phason disordered two dimensional quantum antiferromagnet

We examine a novel type of disorder in quantum antiferromagnets. Our model consists of localized spins with antiferromagnetic exchanges on a bipartite quasiperiodic structure, which is geometrically disordered in such a way that no frustration is introduced. In the limit of zero disorder, the structure is the perfect Penrose rhombus tiling. This tiling is progressively disordered by augmenting the number of random "phason flips" or local tile-reshuffling operations. The ground state remains N\'eel ordered, and we have studied its properties as a function of increasing disorder using linear spin wave theory and quantum Monte Carlo. We find that the ground state energy decreases, indicating enhanced quantum fluctuations with increasing disorder. The magnon spectrum is progressively smoothed, and the effective spin wave velocity of low energy magnons increases with disorder. For large disorder, the ground state energy as well as the average staggered magnetization tend towards limiting values characteristic of this type of randomized tilings.Comment: 5 pages, 7 figure

Geometry fluctuations in a two-dimensional quantum antiferromagnet

The paper considers the effects of random fluctuations of the local spin connectivities (fluctuations of the geometry) on ground state properties of a two-dimensional quantum antiferromagnet. We analyse the behavior of spins described by the Heisenberg model as a function of what we call phason flip disorder, following a terminology used for aperiodic systems. The calculations were carried out both within linear spin wave theory and using quantum Monte Carlo simulations. An "order by disorder" phenomenon is observed in this model, wherein antiferromagnetism is found to be enhanced by phason disorder. The value of the staggered order parameter increases with the number of defects, accompanied by an increase in the ground state energy of the system.Comment: 5 pages, 7 figures. Shortened and corrected version (as accepted for publication in Physical Review B